I received an email reply from Oppo technical assistance.
While they don't officially list the Classic as a supported iPod model for HA-2 connection via USB, they admit it does work but could need coaxing in terms of getting the initialization handshake to occur. Things like power cycling either the HA-2, or the iPod, or connecting/reconnecting the 30-pin cable in a particular sequence. This is because the Classic uses an older version of MFI authentication than the HA-2 was designed for.
That said, I received my HA-2 yesterday and have had no such fussy connection issues at all, using an iFlash modified 128GB SDXC Gen. 6 Classic: